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Kurt Gödel

Kurt Gödel
Kurt Friedrich Gödel (/ˈkɜrt ɡɜrdəl/; German: [ˈkʊʁt ˈɡøːdəl] ( ); April 28, 1906 – January 14, 1978) was an Austrian, and later American, logician, mathematician, and philosopher. Considered with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell,[1] A. N. Whitehead,[1] and David Hilbert were pioneering the use of logic and set theory to understand the foundations of mathematics. Gödel published his two incompleteness theorems in 1931 when he was 25 years old, one year after finishing his doctorate at the University of Vienna. He also showed that neither the axiom of choice nor the continuum hypothesis can be disproved from the accepted axioms of set theory, assuming these axioms are consistent. Life[edit] Childhood[edit] In his family, young Kurt was known as Herr Warum ("Mr. Studying in Vienna[edit]

John von Neumann John von Neumann (/vɒn ˈnɔɪmən/; December 28, 1903 – February 8, 1957) was a Hungarian and later American pure and applied mathematician, physicist, inventor, polymath, and polyglot. He made major contributions to a number of fields,[2] including mathematics (foundations of mathematics, functional analysis, ergodic theory, geometry, topology, and numerical analysis), physics (quantum mechanics, hydrodynamics, and fluid dynamics), economics (game theory), computing (Von Neumann architecture, linear programming, self-replicating machines, stochastic computing), and statistics.[3] He was a pioneer of the application of operator theory to quantum mechanics, in the development of functional analysis, a principal member of the Manhattan Project and the Institute for Advanced Study in Princeton (as one of the few originally appointed), and a key figure in the development of game theory[2][4] and the concepts of cellular automata,[2] the universal constructor, and the digital computer. . and

Alan Turing - Wikipedia English computer scientist (1912–1954) Alan Mathison Turing OBE FRS (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher and theoretical biologist.[5] Turing was highly influential in the development of theoretical computer science, providing a formalisation of the concepts of algorithm and computation with the Turing machine, which can be considered a model of a general-purpose computer.[6][7][8] He is widely considered to be the father of theoretical computer science and artificial intelligence.[9] Born in Maida Vale, London, Turing was raised in southern England. He graduated from King's College, Cambridge, with a degree in mathematics. Whilst he was a fellow at Cambridge, he published a proof demonstrating that some purely mathematical yes–no questions can never be answered by computation. He defined a Turing machine and proved that the halting problem for Turing machines is undecidable. Early life and education Family

Ludwig Boltzmann Ludwig Eduard Boltzmann (February 20, 1844 – September 5, 1906) was an Austrian physicist and philosopher whose greatest achievement was in the development of statistical mechanics, which explains and predicts how the properties of atoms (such as mass, charge, and structure) determine the physical properties of matter (such as viscosity, thermal conductivity, and diffusion). Biography[edit] Childhood and education[edit] Boltzmann was born in Vienna, the capital of the Austrian Empire. Boltzmann studied physics at the University of Vienna, starting in 1863. Academic career[edit] In 1869 at age 25, thanks to a letter of recommendation written by Stefan,[1] he was appointed full Professor of Mathematical Physics at the University of Graz in the province of Styria. Ludwig Boltzmann and co-workers in Graz, 1887. In 1872, long before women were admitted to Austrian universities, he met Henriette von Aigentler, an aspiring teacher of mathematics and physics in Graz. Final years[edit] Physics[edit]

David Hilbert _ wikipedia German mathematician (1862–1943) David Hilbert (;[4] German: [ˈdaːvɪt ˈhɪlbɐt]; 23 January 1862 – 14 February 1943) was a German mathematician and one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics (particularly proof theory). Hilbert adopted and defended Georg Cantor's set theory and transfinite numbers. In 1900, he presented a collection of problems that set the course for much of the mathematical research of the 20th century.[5][6] Hilbert and his students contributed significantly to establishing rigor and developed important tools used in modern mathematical physics. Life[edit] Early life and education[edit] Death[edit]

Loi de Poisson Un article de Wikipédia, l'encyclopédie libre. La loi de Poisson a été introduite en 1838 par Siméon Denis Poisson (1781–1840), dans son ouvrage Recherches sur la probabilité des jugements en matière criminelle et en matière civile[2]. Le sujet principal de cet ouvrage consiste en certaines variables aléatoires N qui dénombrent, entre autres choses, le nombre d'occurrences (parfois appelées « arrivées ») qui prennent place pendant un laps de temps donné. Si le nombre moyen d'occurrences dans cet intervalle est λ, alors la probabilité qu'il existe exactement k occurrences (k étant un entier naturel, k = 0, 1, 2, ...) est où e est la base de l'exponentielle (2,718...)k! On dit alors que X suit la loi de Poisson de paramètre λ. Calcul de p(k)[modifier | modifier le code] Ce calcul peut se faire de manière déductive en travaillant sur une loi binomiale de paramètres (T; λ/T). Il peut aussi se faire de manière inductive en étudiant sur l'intervalle [0; T] les fonctions On note Remarques : et

Bertrand Russell _ wikipedia Russell led the British "revolt against idealism" in the early 20th century.[58] He is considered one of the founders of analytic philosophy along with his predecessor Gottlob Frege, colleague G. E. Moore, and his protégé Ludwig Wittgenstein. He is widely held to be one of the 20th century's premier logicians.[55] With A. Russell was a prominent anti-war activist; he championed anti-imperialism[60][61] and went to prison for his pacifism during World War I.[62] Later, he campaigned against Adolf Hitler, then criticised Stalinist totalitarianism, attacked the involvement of the United States in the Vietnam War, and was an outspoken proponent of nuclear disarmament.[63] In 1950 Russell was awarded the Nobel Prize in Literature "in recognition of his varied and significant writings in which he champions humanitarian ideals and freedom of thought Biography Early life and background Young Bertrand Russell Childhood and adolescence University and first marriage Early career Russell in 1907.

Andreï Kolmogorov Un article de Wikipédia, l'encyclopédie libre. Andreï Nikolaïevitch Kolmogorov Andreï Nikolaïevitch Kolmogorov (en russe : Андрей Николаевич Колмогоров ; 25 avril 1903 à Tambov - 20 octobre 1987 à Moscou) est un mathématicien soviétique et russe dont les apports en mathématiques sont considérables. Biographie[modifier | modifier le code] Enfance[modifier | modifier le code] Kolmogorov est né à Tambov en 1903. Kolmogorov fut scolarisé à l'école du village de sa tante, et ses premiers efforts littéraires et articles mathématiques furent imprimés dans le journal de l'école. Carrière[modifier | modifier le code] Après avoir terminé ses études secondaires en 1920, il suit les cours à l'Université de Moscou et à l'institut Mendeleïev. Après la fin de ses études supérieures en 1925, il commence son doctorat auprès de Nikolaï Louzine, qu’il termine en 1929. La même année, il devient directeur de l'Institut de mathématiques de l'université de Moscou. Contributions[modifier | modifier le code]

Gottlob Frege _ wikipedia German philosopher, logician, and mathematician (1848–1925) Friedrich Ludwig Gottlob Frege (;[15] German: [ˈɡɔtloːp ˈfreːɡə]; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language, logic, and mathematics. Though he was largely ignored during his lifetime, Giuseppe Peano (1858–1932), Bertrand Russell (1872–1970), and, to some extent, Ludwig Wittgenstein (1889–1951) introduced his work to later generations of philosophers. Frege is widely considered to be the greatest logician since Aristotle, and one of the most profound philosophers of mathematics ever.[16] Life[edit] Childhood (1848–69)[edit] Frege was born in 1848 in Wismar, Mecklenburg-Schwerin (today part of Mecklenburg-Vorpommern). In childhood, Frege encountered philosophies that would guide his future scientific career. 1918–19.

Wiener Kreis De Wiener Kreis (Nederlands: Weense cirkel of Weense kring) (1920-1938) was een groep filosofen en wetenschappers die zich rond Moritz Schlick schaarden. Centrale figuren waren de econoom Otto Neurath, de filosoof Friedrich Waismann en de filosoof Rudolf Carnap. Ludwig Wittgenstein en Karl Popper waren regelmatig bij samenkomsten aanwezig, maar zij waren geen leden van de groep daar zij op essentiële punten afweken van het door de groep gepropageerde logisch positivisme oftewel logisch empirisme. Andere leden waren Gustav Bergmann, Herbert Feigl, Philipp Frank, Kurt Gödel, Hans Hahn, Eino Kaila, Victor Kraft, Karl Menger, Marcel Natkin, Olga Hahn-Neurath, Theodor Radakovic en Rose Rand. Twee boeken lagen aan de basis van de ontwikkelingen van deze stroming, namelijk Wittgensteins Tractatus Logico-Philosophicus (1921), en Carnaps Der logische Aufbau der Welt (1926). Doelstellingen en thema's[bewerken | brontekst bewerken] Bibliografie[bewerken | brontekst bewerken]

Hilbert's program From Wikipedia, the free encyclopedia Attempt to formalize all of mathematics, based on a finite set of axioms In mathematics, Hilbert's program, formulated by German mathematician David Hilbert in the early 1920s,[1] was a proposed solution to the foundational crisis of mathematics, when early attempts to clarify the foundations of mathematics were found to suffer from paradoxes and inconsistencies. Gödel's incompleteness theorems, published in 1931, showed that Hilbert's program was unattainable for key areas of mathematics. Statement of Hilbert's program[edit] The main goal of Hilbert's program was to provide secure foundations for all mathematics. Gödel's incompleteness theorems[edit] Kurt Gödel showed that most of the goals of Hilbert's program were impossible to achieve, at least if interpreted in the most obvious way. Hilbert's program after Gödel[edit] See also[edit] References[edit] G. External links[edit] Richard Zach.

L. E. J. Brouwer Dutch mathematician and logician Luitzen Egbertus Jan Brouwer (; Dutch: [ˈlœy̯tsə(n) ɛɣˈbɛrtəs jɑn ˈbrʌu̯ər]; 27 February 1881 – 2 December 1966), usually cited as L. E. J. Brouwer but known to his friends as Bertus, was a Dutch mathematician and philosopher who worked in topology, set theory, measure theory and complex analysis.[2][4][5] Regarded as one of the greatest mathematicians of the 20th century,[6] he is known as the founder of modern topology,[7] particularly for establishing his fixed-point theorem and the topological invariance of dimension.[8] Biography[edit] Brouwer was born to Dutch Protestant parents.[9] Early in his career, Brouwer proved a number of theorems in the emerging field of topology. Brouwer also proved the simplicial approximation theorem in the foundations of algebraic topology, which justifies the reduction to combinatorial terms, after sufficient subdivision of simplicial complexes, of the treatment of general continuous mappings. "... Bibliography[edit]